We investigate non-geometric sharp permutation groups of type {0,k} whose point stabilizers are certain Frobenius groups. We show that if a point stabilizer has a cyclic Frobenius kernel whose order is a power of a prime and Frobenius complement cyclic of prime order, then the point stabilizer is isomorphic to the symmetric group on 3 letters, and there is up to permutation isomorphism, one such permutation group. Further, we determine a significant structural description of non-geometric sharp permutation groups of type {0,k} whose point stabilizers are Frobenius groups with elementary abelian Frobenius kernel K and Frobenius complement L with |L| = |K|-1. As a result of this structural description, it is shown that the smallest non-solvable Frobenius group cannot be a point stabilizer in a non-geometric sharp permutation group of type {0,k}.
| Identifer | oai:union.ndltd.org:unt.edu/info:ark/67531/metadc2137593 |
| Date | 05 1900 |
| Creators | Norman, Blake Addison |
| Contributors | Brozovic, Douglas, Conley, Charles, Schmidt, Ralf |
| Publisher | University of North Texas |
| Source Sets | University of North Texas |
| Language | English |
| Detected Language | English |
| Type | Thesis or Dissertation |
| Format | Text |
| Rights | Public, Norman, Blake Addison, Copyright, Copyright is held by the author, unless otherwise noted. All rights Reserved. |
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